Finite Group Databasebeta

C2×#22558191 #30765646

order17152
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#22558191

Splittings

SylowC67 ⋊ C2×#1338

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic67
commutatorC2×C4×C67C22×C8
FrattiniC4×C8C22×D67
FittingC2×#446×C67C2
socle, prime radicalC23×C67C22⋊C8
cosocleC4×C8×C67C23
hypercenterC2×#446D67
hypocenterC67C2×#1338
LCSG ▷ C2×C4×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#446

346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

1924 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 79383);