Finite Group Databasebeta

C22×Q8×C67⋊C8 #31720183

order17152
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productC22×Q8×C67⋊C8

Splittings

SylowC67 ⋊ C22×C8×Q8

Subgroups

subgroupG/H
centerC23×C4C22×D67
commutatorC2×C67C24×C8
FrattiniC2×C4C24×D67
FittingC22×C4×Q8×C67C2
socle, prime radicalC24×C67C22×C4
cosocleC2×C4×C67C25
hypercenterC22×C4×Q8D67
hypocenterC67C22×C8×Q8
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C23×C4 ◁ C22×C4×Q8

2478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1033920);