Finite Group Databasebeta

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C2×#19097727 #23757726

order10048
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#19097727

Splittings

SylowC157 ⋊ C2×#117

Subgroups

subgroupG/H
centerC23C22×D157
commutatorC2×C157C23×C4
FrattiniC22C23×D157
FittingC2×C22⋊C4×C157C2
socleC23×C157C23
prime radicalC24×C157C22
cosocleC22×C157C24
hypercenterC2×C22⋊C4D157
hypocenterC157C2×#117
LCSG ▷ C2×C157 ▷ C157
UCSC1 ◁ C23 ◁ C2×C22⋊C4

330 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1600 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#34098447, #34098467, #34099867, …
maximal normal subgroup of#34098447, #34098467, #34099867, …
maximal quotient ofC2×#23757118, C2×C22⋊C4×Dic157, C2×#23757124, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10048, 1002);