Finite Group Databasebeta

C2×#17986113 #22597227

order9088
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#17986113

Splittings

FittingC2×#104×C71 ⋊ C2
SylowC71 ⋊ C2×#443

Subgroups

subgroupG/H
centerC2×C4D4×D71
commutatorC4×C71C23×C4
FrattiniC2×C4C23×D71
FittingC2×#104×C71C2
socleC22×C71C4×D4
hypercenterC2×#104D71
hypocenterC71C2×#443
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

472 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1036 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×#17986113, #31996003, #31996010, …
maximal normal subgroup ofC4×#17986113, #31996003, #31996010, …
maximal quotient ofC2×#22587132, C2×#22587137, C2×#22587143, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9088, 13397);