Finite Group Databasebeta

#2888×D67 #31719322

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

Aliases

direct product#2888×D67

Splittings

FittingC67×#2888 ⋊ C2
SylowC67 ⋊ C2×#2888

Subgroups

subgroupG/H
centerC2C22×C22⋊C4×D67
commutatorC22×C67C24×C4
FrattiniC2×C4C24×D67
FittingC67×#2888C2
socleC2×C67C23×C22⋊C4
prime radicalC2×H(5,𝔽2)×D67C2
cosocleC2×C4×C67C25
hypercenter#2888D67
hypocenterC67C2×#2888
LCSG ▷ C22×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2 ◁ C2×#41 ◁ #2888

5114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1072

Conjugacy classes & character table

1435 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1033059);