Finite Group Databasebeta

C2×#19134770 #25097057

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#19134770

Splittings

SylowC43 ⋊ C2×#1849

Subgroups

subgroupG/H
centerC22×C4C2×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×#97×C43C2
socleC23×C43C2×C4⋊C4
prime radicalC24×C43C2×Q8
cosocleC22×C4×C43C24
hypercenterC22×#97D43
hypocenterC43C2×#1849
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×#97

1006 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 170028);