Finite Group Databasebeta

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C2×#19128751 #24923249

order10688
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#19128751

Splittings

SylowC167 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22C22⋊Dic167
commutatorC22×C167C22×C4
FrattiniC2×C4C22×D167
FittingC22×Q8×C167C2
socleC22×C167C22⋊C4
prime radicalC23×C167C2×C4
cosocleC2×C4×C167C23
hypercenterC22×Q8D167
hypocenterC167C2×#101
LCSG ▷ C22×C167 ▷ C2×C167 ▷ C167
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

146 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1682 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#36322264, #36322265, C4×#19128751, …
maximal normal subgroup of#36322264, #36322265, C4×#19128751, …
maximal quotient ofC2×#24922995, #36322462, #36322468, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10688, 529);