Finite Group Databasebeta

C2×#15690730 #20260721

order6208
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#15690730

Splittings

FittingC2×C4⋊C4×C97 ⋊ C2
SylowC97 ⋊ C2×#102

Subgroups

subgroupG/H
centerC23C22⋊D97
commutatorC4×C97C22×C4
FrattiniC2×C4C22×D97
FittingC2×C4⋊C4×C97C2
socleC23×C97D4
hypercenterC2×C4⋊C4D97
hypocenterC97C2×#102
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

202 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#27141550, C4×#15690730, #27141560, …
maximal normal subgroup of#27141550, C4×#15690730, #27141560, …
maximal quotient ofC2×#20260462, #27140134, #27140160, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6208, 535);