Finite Group Databasebeta

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C2×#19097690 #23757253

order10048
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#19097690

Splittings

SylowC157 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22C22⋊Dic157
commutatorC22×C157C22×C4
FrattiniC2×C4C22×D157
FittingC22×Q8×C157C2
socleC22×C157C22⋊C4
prime radicalC23×C157C2×C4
cosocleC2×C4×C157C23
hypercenterC22×Q8D157
hypocenterC157C2×#101
LCSG ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

146 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1582 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#34098262, #34098263, C4×#19097690, …
maximal normal subgroup of#34098262, #34098263, C4×#19097690, …
maximal quotient ofC2×#23756999, #34098460, #34098466, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10048, 529);