Finite Group Databasebeta

#3176×D67 #31725657

order17152
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct product#3176×D67

Splittings

FittingC67×#3176 ⋊ C2
SylowC67 ⋊ C2×#3176

Subgroups

subgroupG/H
centerC22C22×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC67×#3176C2
socleC22×C67C23×D4
hypercenter#3176D67
hypocenterC67C2×#3176
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ #117 ◁ #3176

2098 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1039394);