Finite Group Databasebeta

C2×#19134543 #25095857

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#19134543

Splittings

SylowC43 ⋊ C2×#1790

Subgroups

subgroupG/H
centerC23#13063294
commutatorC23×C43C23×C4
FrattiniC24C23×D43
Fitting, prime radicalC22×H(5,𝔽2)×C43C2
socleC23×C43#120
cosocleC24×C43C24
hypercenterC22×H(5,𝔽2)D43
hypocenterC43C2×#1790
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C25 ◁ C22×H(5,𝔽2)

4402 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1492 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 168828);