Finite Group Databasebeta

← Prev (#44568537) Next (#44568539) →

C3×C5×C72×Dic11 #44568538

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C72 · Schur multiplier (H2) = C7

Aliases

direct productC3×C5×C72×Dic11

Splittings

derived, SylowC11 ⋊ C3×C4×C5×C72
HallC3×C5×C72×C11 ⋊ C4
HallC5×C72×C11 ⋊ C3×C4
HallC3×C72×C11 ⋊ C4×C5
HallC72×C11 ⋊ C3×C4×C5
HallC3×C5×C11 ⋊ C4×C72
HallC5×C11 ⋊ C3×C4×C72
HallC3×C11 ⋊ C4×C5×C72

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C72D11
commutator, hypocenterC11C3×C4×C5×C72
FrattiniC2C3×C5×C72×D11
Fitting, socle, prime radicalC2×C3×C5×C72×C11C2
cosocleC2×C11C2×C3×C5×C72
LCSG ▷ C11
UCSC1 ◁ C2×C3×C5×C72

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32340

Conjugacy classes & character table

10290 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 240);