Finite Group Databasebeta

C2×#17989584 #22626559

order9344
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#17989584

Splittings

FittingC2×#41×C73 ⋊ C4
SylowC73 ⋊ C2×#421

Subgroups

subgroupG/H
centerC22C2×C22⋊#64408
commutatorC4×C73C23×C4
FrattiniC4C23×#64408
FittingC2×#41×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC2×#41#64408
hypocenterC73C2×#421
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

772 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

404 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#34008514, #34008516, #34008531, …
maximal normal subgroup of#34008514, #34008516, #34008531, …
maximal quotient ofC2×#22625231, C2×#22625234, C2×#22625226, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9344, 21138);