Finite Group Databasebeta

#1899×D67 #30857614

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4

Aliases

direct product#1899×D67

Splittings

FittingC67×#1899 ⋊ C2
SylowC67 ⋊ C2×#1899

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D67
commutatorC23×C67C23×C4
FrattiniC24C23×D67
FittingC67×#1899C2
socleC22×C67C22×C22⋊C4
prime radicalC22×D4×D67C22
cosocleC24×C67C24
hypercenter#1899D67
hypocenterC67C2×#1899
LCSG ▷ C23×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1899

2066 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

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, 171351);