Finite Group Databasebeta

C2×#22612270 #33244167

order18688
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C27×C42

Aliases

direct productC2×#22612270

Splittings

FittingC2×#376×C73 ⋊ C2
SylowC73 ⋊ C2×C4×#117

Subgroups

subgroupG/H
centerC23×C4C22×D73
commutatorC2×C73C23×C42
FrattiniC23C24×D73
FittingC2×#376×C73C2
socleC24×C73C24
prime radicalC24×D73C23
cosocleC23×C73C25
hypercenterC2×#376D73
hypocenterC73C2×C4×#117
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C23×C4 ◁ C2×#376

4462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9344

Conjugacy classes & character table

3040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 327751);