Finite Group Databasebeta

C2×#22558270 #30767195

order17152
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#22558270

Splittings

SylowC67 ⋊ C2×#1366

Subgroups

subgroupG/H
centerC22#16863145
commutatorC42×C67C22×C4
FrattiniC4×C8C22×D67
FittingC2×#499×C67C2
socleC22×C67#333
prime radicalC23×C67#100
cosocleC4×C8×C67C23
hypercenterC2×#499D67
hypocenterC67C2×#1366
LCSG ▷ C42×C67 ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#499

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1498 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 80932);