Finite Group Databasebeta

#15690865

order3104
automorphism?
homologyAbelianization (H1) = C42 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC97 ⋊ #97

Subgroups

subgroupG/H
center, FrattiniC22C2×#87604
commutatorC2×C97C42
FittingC2×C4×C97C4
socle, prime radicalC22×C97C2×C4
cosocleC2×Dic97C22
hypercenterC2×C4#87604
hypocenterC97#97
LCSG ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C2×C4

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3104

Polycyclic presentation:

2^5,97|a^2=c,b^2=d,c^2=e,b^a=be,f^a=f^22,f^c=f^96

Conjugacy classes & character table

212 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3104, 201);