Finite Group Databasebeta

C2×#19136280 #25249427

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#19136280

Splittings

SylowC43 ⋊ C2×#2132

Subgroups

subgroupG/H
centerC2×C4#13063240
commutatorC2×C4×C43C23×C4
FrattiniC2×Q8C23×D43
Fitting, prime radicalC2×C43×#532C2
socleC22×C43C2×#99
cosocleC2×Q8×C43C24
hypercenterC2×#532D43
hypocenterC43C2×#2132
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×#41 ◁ C2×#532

1306 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1228 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322398);