Finite Group Databasebeta

C2×#22568775 #31719456

order17152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#22568775

Splittings

SylowC67 ⋊ C2×#2906

Subgroups

subgroupG/H
centerC22×C4C23×D67
commutatorC22×C67C24×C4
FrattiniC2×C4C24×D67
FittingC22×#131×C67C2
socleC23×C67C23×C4
prime radicalC22×#41×C67C22
cosocleC2×C4×C67C25
hypercenterC22×#131D67
hypocenterC67C2×#2906
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C22×#131

2810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

2740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1033193);