Finite Group Databasebeta

C8×#14556563 #33092008

order18688
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC8×#14556563

Splittings

FittingC2×C8×D4×C73 ⋊ C2
SylowC73 ⋊ C8×#121

Subgroups

subgroupG/H
centerC22×C8C22×D73
commutatorC22×C73C23×C8
FrattiniC22×C4C23×D73
FittingC2×C8×D4×C73C2
socleC23×C73C23×C4
prime radicalC2×#14556563C4
cosocleC22×C4×C73C24
hypercenterC2×C8×D4D73
hypocenterC73C8×#121
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C8 ◁ C2×C8×D4

1222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9344

Conjugacy classes & character table

2992 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 175592);