Finite Group Databasebeta

#2916×D67 #31719525

order17152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct product#2916×D67

Splittings

FittingC67×#2916 ⋊ C2
SylowC67 ⋊ C2×#2916

Subgroups

subgroupG/H
centerC4C22×D4×D67
commutatorC4×C67C24×C4
FrattiniC2×C4C24×D67
FittingC67×#2916C2
socleC2×C67C23×C4⋊C4
prime radicalC2×#41×D67C22
cosocleC2×C4×C67C25
hypercenter#2916D67
hypocenterC67C2×#2916
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C4 ◁ C2×#41 ◁ #2916

2586 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, 1033262);