Finite Group Databasebeta

C2×#22574012 #31763735

order17152
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#22574012

Splittings

SylowC67 ⋊ C2×#3501

Subgroups

subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC22×C4×D4×C67C2
socleC23×C67C25
prime radicalC23×D4×C67C22
hypercenterC22×C4×D4D67
hypocenterC67C2×#3501
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C22×C4×D4

7738 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

2728 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1077472);