Finite Group Databasebeta

C2×#22568672 #31719304

order17152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#22568672

Splittings

FittingC2×#519×C67 ⋊ C2
SylowC67 ⋊ C2×#2884

Subgroups

subgroupG/H
centerC22C22×(C2×D67)⋊C4
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC2×#519×C67C2
socleC22×C67C22×C22⋊C4
prime radicalC22×#14524091C2
cosocleC23×C67C25
hypercenterC2×#519D67
hypocenterC67C2×#2884
LCSG ▷ C22×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C23×Q8 ◁ C2×#519

4818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

2326 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1033041);