Finite Group Databasebeta

#3002×D67 #31722162

order17152
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct product#3002×D67

Splittings

FittingC67×#3002 ⋊ C2
SylowC67 ⋊ C2×#3002

Subgroups

subgroupG/H
centerC2×C4C2×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC67×#3002C2
socleC22×C67C23×D4
hypercenter#3002D67
hypocenterC67C2×#3002
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3002

5130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

1330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1035899);