Finite Group Databasebeta

C2×#19104691 #23782118

order10432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#19104691

Splittings

SylowC163 ⋊ C2×#117

Subgroups

subgroupG/H
centerC23C22×D163
commutatorC2×C163C23×C4
FrattiniC22C23×D163
FittingC2×C22⋊C4×C163C2
socleC23×C163C23
prime radicalC24×C163C22
cosocleC22×C163C24
hypercenterC2×C22⋊C4D163
hypocenterC163C2×#117
LCSG ▷ C2×C163 ▷ C163
UCSC1 ◁ C23 ◁ C2×C22⋊C4

330 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1660 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#35212847, #35212867, #35214267, …
maximal normal subgroup of#35212847, #35212867, #35214267, …
maximal quotient ofC2×#23781510, C2×C22⋊C4×Dic163, C2×#23781516, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10432, 1002);