Finite Group Databasebeta

C2×C8×C4⋊#64408 #34020181

order18688
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C8×C4⋊#64408

Splittings

FittingC2×C4×C8×C73 ⋊ C4
SylowC73 ⋊ C2×C8×C4⋊C4

Subgroups

subgroupG/H
centerC22×C8C2×#64408
commutatorC2×C73C22×C4×C8
FrattiniC2×C4C23×#64408
FittingC2×C4×C8×C73C4
socleC23×C73C2×C42
prime radicalC23×D73C22×C4
cosocleC2×C4×D73C24
hypercenterC2×C4×C8#64408
hypocenterC73C2×C8×C4⋊C4
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

1438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4672

Conjugacy classes & character table

1312 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1103765);