Finite Group Databasebeta

C2×C4×#14556124 #32155964

order18176
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×C4×#14556124

Splittings

FittingC22×C4×D4×C71 ⋊ C2
SylowC71 ⋊ C2×C4×#127

Subgroups

subgroupG/H
centerC23×C4C22×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC22×C4×D4×C71C2
socleC24×C71C24
prime radicalC22×#14556124C2
cosocleC23×C71C25
hypercenterC22×C4×D4D71
hypocenterC71C2×C4×#127
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23×C4 ◁ C22×C4×D4

5694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

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, 328080);