Finite Group Databasebeta

#15692182

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

Aliases

No aliases for this group.

Splittings

SylowC101 ⋊ #104

Subgroups

subgroupG/H
centerC4C22⋊D101
commutatorC4×C101C2×C4
FrattiniC2×C4C2×D101
Fitting, prime radical#41×C101C2
socleC2×C101C22⋊C4
cosocleC2×C4×C101C22
hypercenter#41D101
hypocenterC101#104
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C4 ◁ C2×C4 ◁ #41

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 808

Polycyclic presentation:

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

Conjugacy classes & character table

514 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3232, 73);