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#34047646

order19072
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4

Aliases

No aliases for this group.

Splittings

SylowC149 ⋊ #2355

Subgroups

subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
FittingC4×C4⋊C4×C149C2
socle, prime radical, cosocleC23×C149C24
hypercenterC4×C4⋊C4D149
hypocenterC149#2355
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C4×C4⋊C4

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19072

Polycyclic presentation:

2^7,149|a^2=g,b^2=ef,c^2=f,d^2=e,b^a=be,c^a=cf,d^b=de,h^b=h^148

Conjugacy classes & character table

3010 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19072, 7465);