Finite Group Databasebeta

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D5×C3⋊(C7⋊D77) #44568914

order32340
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C7

Aliases

direct productD5×C3⋊(C7⋊D77)
unambiguous semidirect product(C3×D5)⋊(C7⋊D77)
unambiguous semidirect product(C7×D5)⋊D231
unambiguous semidirect product(D5×C11)⋊(C3⋊(C7⋊D7))

Splittings

Fitting, socle, derived, HallC3×C5×C72×C11 ⋊ C22
HallC5×C72×C11 ⋊ C2×D3
HallC3×C72×C11 ⋊ C2×D5
HallC3×C5×C72 ⋊ C2×D11
HallC72×C11 ⋊ D3×D5
HallC5×C72 ⋊ C2×D33
HallC3×C5×C11 ⋊ C2×C7⋊D7
HallC3×C72 ⋊ D5×D11
HallC5×C11 ⋊ C2×C3⋊(C7⋊D7)
SylowC72 ⋊ D5×D33
HallC3×C11 ⋊ D5×C7⋊D7
HallC3×C5 ⋊ C2×C7⋊D77
SylowC11 ⋊ D5×C3⋊(C7⋊D7)
SylowC5 ⋊ C2×C3⋊(C7⋊D77)
SylowC3 ⋊ D5×C7⋊D77

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C72×C11C22
LCSG ▷ C3×C5×C72×C11
UCSC1

400 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

3240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 616);