Finite Group Databasebeta

#44472209

order29984
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4

Aliases

No aliases for this group.

Splittings

SylowC937 ⋊ #117

Subgroups

subgroupG/H
centerC2×C4C2×D937
commutatorC2×C937C22×C4
FrattiniC22C22×D937
FittingC22×C4×C937C2
socle, cosocleC22×C937C23
prime radicalC23×C937C22
hypercenterC22×C4D937
hypocenterC937#117
LCSG ▷ C2×C937 ▷ C937
UCSC1 ◁ C2×C4 ◁ C22×C4

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14992

Polycyclic presentation:

2^5,937|a^2=e,c^2=d,b^a=bd,f^a=f^936

Conjugacy classes & character table

7508 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29984, 105);