Finite Group Databasebeta

C8×(C2×#64408)⋊C4 #34008247

order18688
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct productC8×(C2×#64408)⋊C4

Splittings

FittingC2×C4×C8×C73 ⋊ C4
SylowC73 ⋊ C8×#95

Subgroups

subgroupG/H
centerC22×C8C2×#64408
commutatorC2×C73C42×C8
FrattiniC22×C4C22×#64408
FittingC2×C4×C8×C73C4
socleC23×C73C2×C42
prime radicalC23×D73C22×C4
cosocleC22×C4×D73C23
hypercenterC2×C4×C8#64408
hypocenterC73C8×#95
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

1174 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, 1091831);