Finite Group Databasebeta

#29504736

order15296
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

No aliases for this group.

Splittings

SylowC239 ⋊ #407

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D239
commutator, socleC22×C239C22×C4
FittingC23×C4×C239C2
prime radicalC24×C239C4
cosocleC2×C4×C239C23
hypercenterC23×C4D239
hypocenterC239#407
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C2×C4 ◁ C23×C4

190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3824

Polycyclic presentation:

2^6,239|a^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^238

Conjugacy classes & character table

3836 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#44482400, #44482401, #44482424, …
maximal normal subgroup of#44482400, #44482401, #44482424, …
maximal quotient of#44482875, #44482878, #44482882, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15296, 513);