Finite Group Databasebeta

#1926×D67 #30858205

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct product#1926×D67

Splittings

FittingC67×#1926 ⋊ C2
SylowC67 ⋊ C2×#1926

Subgroups

subgroupG/H
centerC23C2×D4×D67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingC67×#1926C2
socleC23×C67C22×D4
prime radicalC22×D4×D67C22
cosocleC22×C4×C67C24
hypercenter#1926D67
hypocenterC67C2×#1926
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1926

1454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

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, 171942);