Finite Group Databasebeta

#37612919

order24736
automorphism?
homologyAbelianization (H1) = C2×C8 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC773 ⋊ C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC2×C4C2×D773
commutatorC2×C773C2×C8
FittingC2×C8×C773C2
socle, prime radicalC22×C773C2×C4
cosocleC2×C4×C773C22
hypercenterC2×C8D773
hypocenterC773C4⋊C8
LCSG ▷ C2×C773 ▷ C773
UCSC1 ◁ C2×C4 ◁ C2×C8

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24736

Polycyclic presentation:

2^5,773|a^2=d,b^2=c,d^2=e,b^a=bc,f^b=f^772

Conjugacy classes & character table

6196 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24736, 75);