Finite Group Databasebeta

C23×C22⋊(C71⋊C8) #32860879

order18176
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C211

Aliases

direct productC23×C22⋊(C71⋊C8)

Splittings

SylowC71 ⋊ C23×C22⋊C8

Subgroups

subgroupG/H
centerC24×C4C2×D71
commutatorC2×C71C24×C8
FrattiniC2×C4C24×D71
FittingC25×C4×C71C2
socleC25×C71C2×C4
prime radicalC26×C71C4
cosocleC2×C4×C71C25
hypercenterC25×C4D71
hypocenterC71C23×C22⋊C8
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C24×C4 ◁ C25×C4

7646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

4640 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 1032995);