Finite Group Databasebeta

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#38743431

order25216
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

No aliases for this group.

Splittings

SylowC197 ⋊ #1939

Subgroups

subgroupG/H
center, FrattiniC22×C4C22×D197
commutatorC22×C197C22×C8
FittingC4×C4⋊C4×C197C2
socle, prime radicalC23×C197C22×C4
cosocleC22×C4×C197C23
hypercenterC4×C4⋊C4D197
hypocenterC197#1939
LCSG ▷ C22×C197 ▷ C197
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

260 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25216

Polycyclic presentation:

2^7,197|a^2=f,b^2=f,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^196,h^b=h^196

Conjugacy classes & character table

3976 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25216, 5229);