Finite Group Databasebeta

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C3×C72×C11×Dic5 #44568533

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C72×C11 · Schur multiplier (H2) = C7

Aliases

direct productC3×C72×C11×Dic5

Splittings

derived, SylowC5 ⋊ C3×C4×C72×C11
HallC3×C5×C72×C11 ⋊ C4
HallC5×C72×C11 ⋊ C3×C4
HallC3×C5×C72 ⋊ C4×C11
HallC5×C72 ⋊ C3×C4×C11
HallC3×C5×C11 ⋊ C4×C72
HallC5×C11 ⋊ C3×C4×C72
HallC3×C5 ⋊ C4×C72×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C72×C11D5
commutator, hypocenterC5C3×C4×C72×C11
FrattiniC2C3×C72×D5×C11
Fitting, socle, prime radicalC2×C3×C5×C72×C11C2
cosocleC2×C5C2×C3×C72×C11
LCSG ▷ C5
UCSC1 ◁ C2×C3×C72×C11

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32340

Conjugacy classes & character table

12936 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 235);