Finite Group Databasebeta

C8×#14524074 #30825256

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

Aliases

direct productC8×#14524074

Splittings

FittingC2×C8×Q8×C67 ⋊ C2
SylowC67 ⋊ C8×#137

Subgroups

subgroupG/H
centerC2×C8C2×C22⋊D67
commutatorC4×C67C23×C8
FrattiniC42C23×D67
FittingC2×C8×Q8×C67C2
socleC22×C67C2×C4×D4
prime radicalC2×#11761628C2×C4
cosocleC42×C67C24
hypercenterC2×C8×Q8D67
hypocenterC67C8×#137
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C8 ◁ C2×C4×C8 ◁ C2×C8×Q8

714 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

2728 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 138993);