Finite Group Databasebeta

C22×C4×(C2×D71)⋊C4 #32155626

order18176
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C210×C4

Aliases

direct productC22×C4×(C2×D71)⋊C4

Splittings

FittingC23×C42×C71 ⋊ C2
SylowC71 ⋊ C22×C4×C22⋊C4

Subgroups

subgroupG/H
centerC24×C4C2×D71
commutatorC2×C71C23×C42
FrattiniC23C24×D71
FittingC23×C42×C71C2
socleC25×C71C23
prime radicalC25×D71C22
cosocleC23×C71C25
hypercenterC23×C42D71
hypocenterC71C22×C4×C22⋊C4
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C24×C4 ◁ C23×C42

9534 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, 327742);