Finite Group Databasebeta

C2×C4×#14556054 #31995165

order18176
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×#14556054

Splittings

FittingC2×C4×M16×C71 ⋊ C2
SylowC71 ⋊ C2×C4×#104

Subgroups

subgroupG/H
centerC2×C42C22⋊D71
commutatorC4×C71C22×C42
FrattiniC22×C4C23×D71
FittingC2×C4×M16×C71C2
socleC23×C71C2×C22⋊C4
prime radicalC22×#11765865C22
cosocleC22×C4×C71C24
hypercenterC2×C4×M16D71
hypocenterC71C2×C4×#104
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C2×C4×M16

1878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4544

Conjugacy classes & character table

2912 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 167281);