Finite Group Databasebeta

#44446303

order29728
automorphism?
homologyAbelianization (H1) = C2×C8 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC929 ⋊ C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC2×C4C2×D929
commutatorC2×C929C2×C8
FittingC2×C8×C929C2
socle, prime radicalC22×C929C2×C4
cosocleC2×C4×C929C22
hypercenterC2×C8D929
hypocenterC929C4⋊C8
LCSG ▷ C2×C929 ▷ C929
UCSC1 ◁ C2×C4 ◁ C2×C8

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29728

Polycyclic presentation:

2^5,929|a^2=d,b^2=c,d^2=e,b^a=bc,f^b=f^928

Conjugacy classes & character table

7444 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29728, 75);