Finite Group Databasebeta

C2×#22586581 #31919110

order18176
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#22586581

Splittings

SylowC71 ⋊ C2×#1438

Subgroups

subgroupG/H
centerC25C22×D71
commutatorC23×C71C23×C4
FrattiniC24C23×D71
Fitting, prime radicalC24×D4×C71C2
socleC25×C71C23
cosocleC24×C71C24
hypercenterC24×D4D71
hypocenterC71C2×#1438
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C25 ◁ C24×D4

8190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2888 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 91226);