Finite Group Databasebeta

#15692172

order3232
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC101 ⋊ #100

Subgroups

subgroupG/H
centerC2C22⋊Dic101
commutatorC22×C101C2×C4
FrattiniC2×C4C2×D101
Fitting, prime radicalC2×D4×C101C2
socleC2×C101C22⋊C4
cosocleC2×C4×C101C22
hypercenterC2×D4D101
hypocenterC101#100
LCSG ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

46 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 808

Polycyclic presentation:

2^5,101|a^2=d,d^2=e,b^a=bc,c^a=ce,f^a=f^100,d^b=de

Conjugacy classes & character table

511 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3232, 63);