Finite Group Databasebeta

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C5×C72×C11×Dic3 #44568527

order32340
automorphism?
homologyAbelianization (H1) = C4×C5×C72×C11 · Schur multiplier (H2) = C7

Aliases

direct productC5×C72×C11×Dic3
unambiguous semidirect productC3⋊(C4×C5×C72×C11)

Splittings

derived, SylowC3 ⋊ C4×C5×C72×C11
HallC3×C5×C72×C11 ⋊ C4
HallC3×C72×C11 ⋊ C4×C5
HallC3×C5×C72 ⋊ C4×C11
HallC3×C5×C11 ⋊ C4×C72
HallC3×C72 ⋊ C4×C5×C11
HallC3×C11 ⋊ C4×C5×C72
HallC3×C5 ⋊ C4×C72×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C72×C11D3
commutator, hypocenterC3C4×C5×C72×C11
FrattiniC2C5×D3×C72×C11
Fitting, socle, prime radicalC2×C3×C5×C72×C11C2
cosocleC2×C3C2×C5×C72×C11
LCSG ▷ C3
UCSC1 ◁ C2×C5×C72×C11

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32340

Conjugacy classes & character table

16170 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 229);