Finite Group Databasebeta

C2×#17986000 #22596852

order9088
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#17986000

Splittings

SylowC71 ⋊ C2×#417

Subgroups

subgroupG/H
centerC23C2×C22⋊D71
commutatorC4×C71C23×C4
FrattiniC2×C4C23×D71
FittingC22×#41×C71C2
socleC23×C71C2×D4
hypercenterC22×#41D71
hypocenterC71C2×#417
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#41

816 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1444 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#31902926, #31902928, #31902969, …
maximal normal subgroup of#31902926, #31902928, #31902969, …
maximal quotient ofC2×#22586727, C2×#22586779, #31963913, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9088, 13022);