Finite Group Databasebeta

C2×#22558592 #30822184

order17152
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#22558592

Splittings

FittingC22×C4×C8×C67 ⋊ C2
SylowC67 ⋊ C2×#1476

Subgroups

subgroupG/H
centerC2×C42D268
commutatorC4×C67C23×C8
FrattiniC42C23×D67
FittingC22×C4×C8×C67C2
socleC23×C67C2×C22⋊C4
prime radicalC22×#11761628C4
cosocleC42×C67C24
hypercenterC22×C4×C8D67
hypocenterC67C2×#1476
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C22×C4×C8

1430 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

4336 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 135921);