Finite Group Databasebeta

C2×#22569319 #31720877

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

Aliases

direct productC2×#22569319

Splittings

FittingC2×C8×Q8×C67 ⋊ C2
SylowC67 ⋊ C2×#2988

Subgroups

subgroupG/H
centerC22×C4C23×D67
commutatorC2×C67C24×C8
FrattiniC2×C4C24×D67
FittingC2×C8×Q8×C67C2
socleC23×C67C23×C4
prime radicalC22×#11761629C4
cosocleC2×C4×C67C25
hypercenterC2×C8×Q8D67
hypocenterC67C2×#2988
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C2×C8×Q8

2434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

2776 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1034614);