Finite Group Databasebeta

C2×#22562114 #31009315

order17152
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#22562114

Splittings

SylowC67 ⋊ C2×#2183

Subgroups

subgroupG/H
centerC22×C8C22×D67
commutatorC22×C67C23×C8
FrattiniC2×C8C23×D67
FittingC2×C4⋊C16×C67C2
socle, prime radicalC23×C67C22×C8
cosocleC2×C8×C67C24
hypercenterC2×C4⋊C16D67
hypocenterC67C2×#2183
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C8 ◁ C2×C4⋊C16

542 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

2752 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 323052);