Finite Group Databasebeta

#15692977

order3296
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4

Aliases

No aliases for this group.

Splittings

SylowC103 ⋊ #117

Subgroups

subgroupG/H
center, FrattiniC22C22×D103
commutatorC2×C103C22×C4
FittingC22⋊C4×C103C2
socle, cosocleC22×C103C23
prime radicalC23×C103C22
hypercenterC22⋊C4D103
hypocenterC103#117
LCSG ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22⋊C4

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1648

Polycyclic presentation:

2^5,103|a^2=e,c^2=d,b^a=bd,f^c=f^102

Conjugacy classes & character table

530 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3296, 102);