Finite Group Databasebeta

#17984798

order4448
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4

Aliases

No aliases for this group.

Splittings

SylowC139 ⋊ #117

Subgroups

subgroupG/H
center, FrattiniC22C22×D139
commutatorC2×C139C22×C4
FittingC22⋊C4×C139C2
socle, cosocleC22×C139C23
prime radicalC23×C139C22
hypercenterC22⋊C4D139
hypocenterC139#117
LCSG ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22⋊C4

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2224

Polycyclic presentation:

2^5,139|a^2=e,c^2=d,b^a=bd,f^c=f^138

Conjugacy classes & character table

710 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4448, 102);