Finite Group Databasebeta

← Prev (#44568525) Next (#44568527) →

C5×C72×Dic33 #44568526

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

Aliases

direct productC5×C72×Dic33
unambiguous semidirect productC3⋊(C5×C72×Dic11)

Splittings

derived, HallC3×C11 ⋊ C4×C5×C72
HallC3×C5×C72×C11 ⋊ C4
HallC5×C72×C11 ⋊ Dic3
HallC3×C72×C11 ⋊ C4×C5
HallC3×C5×C72 ⋊ Dic11
HallC72×C11 ⋊ C5×Dic3
HallC3×C5×C11 ⋊ C4×C72
HallC3×C72 ⋊ C5×Dic11
HallC5×C11 ⋊ C72×Dic3
HallC3×C5 ⋊ C72×Dic11
SylowC11 ⋊ C5×C72×Dic3
SylowC3 ⋊ C5×C72×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C72D33
commutator, hypocenterC3×C11C4×C5×C72
FrattiniC2C5×C72×D33
Fitting, socle, prime radicalC2×C3×C5×C72×C11C2
cosocleC2×C3×C11C2×C5×C72
LCSG ▷ C3×C11
UCSC1 ◁ C2×C5×C72

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32340

Conjugacy classes & character table

8820 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 228);