Finite Group Databasebeta

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C3×C5⋊D5×D77 #37528628

order23100
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5

Aliases

direct productC3×C5⋊D5×D77

Splittings

Fitting, socle, HallC3×C52×C7×C11 ⋊ C22
derived, HallC52×C7×C11 ⋊ C22×C3
HallC3×C52×C11 ⋊ C2×D7
HallC3×C52×C7 ⋊ C2×D11
HallC52×C11 ⋊ C2×C3×D7
HallC3×C7×C11 ⋊ C2×C5⋊D5
HallC52×C7 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×C3×C5⋊D5
HallC3×C52 ⋊ C2×D77
HallC3×C11 ⋊ D7×C5⋊D5
SylowC52 ⋊ C2×C3×D77
HallC3×C7 ⋊ D11×C5⋊D5
SylowC11 ⋊ C3×D7×C5⋊D5
SylowC7 ⋊ C3×D11×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC3C5⋊D5×D77
commutator, cosocle, hypocenterC52×C7×C11C22×C3
FrattiniC1G
Fitting, socleC3×C52×C7×C11C22
LCSG ▷ C52×C7×C11
UCSC1 ◁ C3

320 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 92 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) = 5775

Conjugacy classes & character table

1680 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 439);