Finite Group Databasebeta

C2×#15690728 #20260714

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

Aliases

direct productC2×#15690728

Splittings

SylowC97 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22#13095488
commutatorC22×C97C22×C4
FrattiniC2×C4C22×D97
FittingC2×M16×C97C2
socleC22×C97C22⋊C4
hypercenterC2×M16D97
hypocenterC97C2×#101
LCSG ▷ C22×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

146 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

982 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#27141531, C4×#15690728, #27141658, …
maximal normal subgroup of#27141531, C4×#15690728, #27141658, …
maximal quotient ofC2×#20260460, #27140059, #27140065, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6208, 528);