Finite Group Databasebeta

C8×#14556622 #33055409

order18688
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC8×#14556622

Splittings

FittingC2×C8×Q8×C73 ⋊ C2
SylowC73 ⋊ C8×#137

Subgroups

subgroupG/H
centerC2×C8C2×C22⋊D73
commutatorC4×C73C23×C8
FrattiniC42C23×D73
FittingC2×C8×Q8×C73C2
socleC22×C73C2×C4×D4
prime radicalC2×#11924028C2×C4
cosocleC42×C73C24
hypercenterC2×C8×Q8D73
hypocenterC73C8×#137
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C8 ◁ C2×C4×C8 ◁ C2×C8×Q8

714 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9344

Conjugacy classes & character table

2968 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 138993);