Finite Group Databasebeta

#37570347

order24448
automorphism?
homologyAbelianization (H1) = C82 · Schur multiplier (H2) = C22×C4

Aliases

No aliases for this group.

Splittings

SylowC191 ⋊ #1273

Subgroups

subgroupG/H
center, FrattiniC2×C42C2×D191
commutatorC2×C191C82
FittingC2×C4×C8×C191C2
socle, prime radicalC23×C191C42
cosocleC2×C42×C191C22
hypercenterC2×C4×C8D191
hypocenterC191#1273
LCSG ▷ C2×C191 ▷ C191
UCSC1 ◁ C2×C42 ◁ C2×C4×C8

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24448

Polycyclic presentation:

2^7,191|a^2=d,b^2=e,d^2=f,e^2=g,b^a=bc,h^b=h^190

Conjugacy classes & character table

6160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 2337);