Finite Group Databasebeta

#44472182

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

Aliases

No aliases for this group.

Splittings

SylowC937 ⋊ #106

Subgroups

subgroupG/H
centerC22D3748
commutatorC4×C937C2×C4
FrattiniC2×C4C2×D937
FittingC2×C8×C937C2
socle, prime radicalC22×C937D4
cosocleC2×C4×C937C22
hypercenterC2×C8D937
hypocenterC937#106
LCSG ▷ C4×C937 ▷ C2×C937 ▷ C937
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29984

Polycyclic presentation:

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

Conjugacy classes & character table

7502 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29984, 78);