Finite Group Databasebeta

C2×#15690729 #20260715

order6208
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#15690729

Splittings

SylowC97 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22C22⋊Dic97
commutatorC22×C97C22×C4
FrattiniC2×C4C22×D97
FittingC22×Q8×C97C2
socleC22×C97C22⋊C4
hypercenterC22×Q8D97
hypocenterC97C2×#101
LCSG ▷ C22×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

146 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

982 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#27139862, #27139863, C4×#15690729, …
maximal normal subgroup of#27139862, #27139863, C4×#15690729, …
maximal quotient ofC2×#20260461, #27140060, #27140066, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6208, 529);