Finite Group Databasebeta

#18012664

order4832
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC151 ⋊ #103

Subgroups

subgroupG/H
centerC22D604
commutatorC4×C151C2×C4
FrattiniC2×C4C2×D151
FittingC2×C8×C151C2
socle, prime radicalC22×C151D4
cosocleC2×C4×C151C22
hypercenterC2×C8D151
hypocenterC151#103
LCSG ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

42 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4832

Polycyclic presentation:

2^5,151|a^2=d,b^2=e,c^2=e,b^a=bc,c^a=ce,f^a=f^150,c^b=ce,f^b=f^150

Conjugacy classes & character table

1214 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4832, 71);