Finite Group Databasebeta

C2×#22625104 #34014580

order18688
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C210

Aliases

direct productC2×#22625104

Splittings

FittingC22×C22⋊C4×C73 ⋊ C4
SylowC73 ⋊ C2×C22⋊#95

Subgroups

subgroupG/H
centerC24C22×#64408
commutatorC22×C73C22×C42
FrattiniC23C23×#64408
FittingC22×C22⋊C4×C73C4
socleC24×C73C22×C4
prime radicalC25×D73C22
cosocleC23×D73C24
hypercenterC22×C22⋊C4#64408
hypocenterC73C2×C22⋊#95
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C24 ◁ C22×C22⋊C4

7630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2336

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1098164);