Finite Group Databasebeta

C2×#22558297 #30770699

order17152
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#22558297

Splittings

SylowC67 ⋊ C2×#1379

Subgroups

subgroupG/H
centerC22×C8D268
commutatorC4×C67C2×C4×C8
FrattiniC22×C8C22×D67
FittingC23×C16×C67C2
socleC23×C67C22⋊C8
prime radicalC24×C67M16
cosocleC22×C8×C67C23
hypercenterC23×C16D67
hypocenterC67C2×#1379
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C8 ◁ C23×C8 ◁ C23×C16

606 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, 84436);