Finite Group Databasebeta

C2×#22562572 #31014053

order17152
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#22562572

Splittings

SylowC67 ⋊ C2×#2276

Subgroups

subgroupG/H
centerC24C23×D67
commutatorC2×C67C23×C42
FrattiniC23C24×D67
FittingC2×#376×C67C2
socle, prime radicalC24×C67C24
cosocleC23×C67C25
hypercenterC2×#376D67
hypocenterC67C2×#2276
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#376

3654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

2776 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 327790);