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C4⋊Q8×C67⋊C8 #30864492

order17152
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC4⋊Q8×C67⋊C8

Splittings

SylowC67 ⋊ C8×C4⋊Q8

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D67
commutatorC22×C67C23×C8
FittingC4×C4⋊Q8×C67C2
socle, prime radicalC23×C67C23×C4
cosocleC22×C4×C67C24
hypercenterC4×C4⋊Q8D67
hypocenterC67C8×C4⋊Q8
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C4×C4⋊Q8

886 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

1960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 178229);