Finite Group Databasebeta

#2896×D67 #31719367

order17152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct product#2896×D67

Splittings

FittingC67×#2896 ⋊ C2
SylowC67 ⋊ C2×#2896

Subgroups

subgroupG/H
centerC2×C4C2×D4×D67
commutatorC4×C67C24×C4
FrattiniC2×C4C24×D67
FittingC67×#2896C2
socleC22×C67C23×D4
prime radicalC22×#41×D67C2
cosocleC2×C4×C67C25
hypercenter#2896D67
hypocenterC67C2×#2896
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2896

5198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

1540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1033104);