Finite Group Databasebeta

C2×#22558051 #30745418

order17152
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#22558051

Splittings

SylowC67 ⋊ C2×#1280

Subgroups

subgroupG/H
centerC24(C2×D67)⋊C4
commutatorC22×C67C2×C4×C8
FrattiniC23×C4C22×D67
FittingC22×C22⋊C8×C67C2
socleC24×C67C22⋊C4
prime radicalC25×C67C2×C4
cosocleC23×C4×C67C23
hypercenterC22×C22⋊C8D67
hypocenterC67C2×#1280
LCSG ▷ C22×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

1390 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, 59155);