Finite Group Databasebeta

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C11⋊C5×D21⋊D7 #44568605

order32340
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC11⋊C5×D21⋊D7
unambiguous semidirect productD21⋊(D7×C11⋊C5)
unambiguous semidirect product(C11×D21⋊D7)⋊C5

Splittings

Fitting, socle, derived, HallC3×C72×C11 ⋊ C22×C5
HallC3×C72×C11⋊C5 ⋊ C22
HallC11×D21⋊D7 ⋊ C5
HallC72×C11⋊C5 ⋊ C2×D3
HallC72×C11 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ D72
HallC3×C72 ⋊ C22×C11⋊C5
SylowC72 ⋊ C2×D3×C11⋊C5
HallC3×C11 ⋊ C5×D72
SylowC11 ⋊ C5×D21⋊D7
SylowC3 ⋊ D72×C11⋊C5

Subgroups

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

208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 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) = 462

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 307);