Finite Group Databasebeta

C2×#22590692 #32155656

order18176
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#22590692

Splittings

FittingC2×C4×C22⋊C4×C71 ⋊ C2
SylowC71 ⋊ C2×#2273

Subgroups

subgroupG/H
centerC24C23×D71
commutatorC2×C71C23×C42
FrattiniC23C24×D71
FittingC2×C4×C22⋊C4×C71C2
socleC24×C71C24
prime radicalC25×D71C22
cosocleC23×C71C25
hypercenterC2×C4×C22⋊C4D71
hypocenterC71C2×#2273
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

5790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4544

Conjugacy classes & character table

2936 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 327772);