Finite Group Databasebeta

C2×#22573771 #31762861

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

Aliases

direct productC2×#22573771

Splittings

FittingC2×C4×#41×C67 ⋊ C2
SylowC67 ⋊ C2×#3475

Subgroups

subgroupG/H
centerC22×C4C23×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×C4×#41×C67C2
socleC23×C67C25
hypercenterC2×C4×#41D67
hypocenterC67C2×#3475
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

7954 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

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, 1076598);