Finite Group Databasebeta

C2×#20299074 #28403763

order14464
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#20299074

Splittings

FittingC2×C4×Q8×C113 ⋊ C2
SylowC113 ⋊ C2×#519

Subgroups

subgroupG/H
centerC23C23×D113
commutatorC2×C113C24×C4
FrattiniC22C24×D113
FittingC2×C4×Q8×C113C2
socleC23×C113C24
prime radicalC23×D113C23
cosocleC22×C113C25
hypercenterC2×C4×Q8D113
hypocenterC113C2×#519
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C2×C4×Q8

1488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

2308 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 17699);