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#44400453

order29056
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

No aliases for this group.

Splittings

SylowC227 ⋊ #1939

Subgroups

subgroupG/H
center, FrattiniC22×C4C22×D227
commutatorC22×C227C22×C8
FittingC4×C4⋊C4×C227C2
socle, prime radicalC23×C227C22×C4
cosocleC22×C4×C227C23
hypercenterC4×C4⋊C4D227
hypocenterC227#1939
LCSG ▷ C22×C227 ▷ C227
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

260 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29056

Polycyclic presentation:

2^7,227|a^2=f,b^2=f,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^226,h^b=h^226

Conjugacy classes & character table

4576 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 5229);