Finite Group Databasebeta

C22×C4⋊C8×D73 #33949590

order18688
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C210

Aliases

direct productC22×C4⋊C8×D73

Splittings

FittingC22×C4⋊C8×C73 ⋊ C2
SylowC73 ⋊ C23×C4⋊C8

Subgroups

subgroupG/H
centerC23×C4C22×D73
commutatorC2×C73C24×C8
FrattiniC2×C4C24×D73
FittingC22×C4⋊C8×C73C2
socleC24×C73C22×C4
prime radicalC24×D73C2×C4
cosocleC2×C4×C73C25
hypercenterC22×C4⋊C8D73
hypocenterC73C23×C4⋊C8
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C23×C4 ◁ C22×C4⋊C8

3870 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9344

Conjugacy classes & character table

3040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1033174);